Typically, by way of nonlimiting example, a high-power laser using a Ti:Al2O3 crystal and based on a chirped pulse amplification (CPA) method generates not only a femtosecond pulse but also nanosecond amplified spontaneous emission (ASE) as well as parasitic pulses, as illustrated on the curve in FIG. 1.
One important characteristic of these lasers is the temporal contrast, defined by the intensity ratio between the ASE pedestal and the femtosecond pulse. For lasers of the 100 TW class, the temporal contrast commonly reaches 6 orders of magnitude, that is to say 10−6.
This type of laser is used, for example, for laser-material interaction experiments. It is then focused with an intensity of 1021 Wcm−2 onto a solid target in order to generate plasma. The ASE can reach an intensity of 1014 Wcm−2 in this case, which is sufficient to pre-ionize the target before the femtosecond pulse arrives. The pulse therefore has to be temporally cleaned: it is necessary to suppress the pre-pulses and to lower the ASE level by at least 3 orders of magnitude. For this type of application, it is important for the temporal contrast to reach at least 10−9.
One solution for improving the temporal contrast consists in using a non-linear filtering technique based on a process of generating an orthogonally polarized wave in a non-linear crystal. This process is linked with the 3rd order non-linear optical susceptibility of cubic crystals: the wave generated with an orthogonal polarization has the same wavelength and is proportional in intensity to the cube of the initial pulse, which is illustrated in FIG. 2. It will be recalled that the intensity IE of a field E is of the form IE=E.E*, E* being the conjugate of E.
The direction of the field E at the entry of the crystal and that of the field E′ at the exit, which is orthogonal to that of E, are represented in FIG. 2a together with their propagation direction Oz. The intensity IE of E and the intensity IE′ of E′, which are represented on the curves in FIG. 2b, illustrate the relation IE′=k.IE3, where k includes the 3rd order susceptibility. The polarizations of the fields appear on the curves: the solid-line curves correspond to the polarization of the incident field and the dashed curves correspond to that of the converted field, which is orthogonal to the former. The temporal contrast thus theoretically passes from a value of 10−6 to 10−18.
FIG. 3a represents an example of such a non-linear filter. The axis z′z represents the propagation axis of the electromagnetic field. At the entry of the filter, the pulse to be cleaned is generated for example by a Ti:Al2O3 laser using a chirped pulse amplifier (CPA). A first polarizer P1 makes it possible to obtain a linearly polarized field E from this pulse. This field is focused by means of an optical focusing system F1 onto a cubic crystal C, that is to say one which does not have a difference in group velocity between the incident field and the generated field, such as a BaF2 crystal which is furthermore transparent over a wide spectral range from the ultraviolet to the infrared. The efficiency of the conversion by the crystal C is proportional to: the length of the crystal×the square of the intensity of the field incident on the crystal. This crystal C, with a length of about 2 mm, converts about 10% of the incident field into a field E′ with a linear polarization orthogonal to that of E. About 90% of the incident field is transmitted by the crystal C without being converted: this unconverted field, with the same polarization as the incident field, carries the ASE. These fields are collimated by a second optical system F2, and a second polarizer P2 is provided in order to cut out the ASE and the unconverted field while transmitting 100% of the converted field E′.
FIG. 4 schematize the improvement of the contrast provided by the filter. The polarizations are identified in the same way as in FIG. 2b. Let IE be the intensity of the field E incident on the crystal C, as represented in FIG. 4a. After the crystal C and before the polarizer P2, FIG. 4b represents the converted field E′ whose intensity IE′ has a contrast of 10−18, and the unconverted residue of IE. After P2, the final filtered signal IE″ is composed of IE′ transmitted fully plus the residue of IE attenuated by the extinction factor T of P2, typically from 10−4 to 10−6. IE″ therefore has a contrast of between 10−10 and 10−12, depending on the value of the extinction factor of P2.
The main limitation of this filter is its longevity and its stability. In fact, the crystal deteriorates at the end of a few hours when it is subjected to an incident field E whose intensity is more than 1012 Wcm−2, the intensity which is necessary in order to obtain a good efficiency of the filter.
There is another limitation of this filter, associated with the self-phase modulation. The high intensity value necessary for good efficiency of the filter also generates modulation of the phase and the amplitude of the spectrum of the femtosecond pulse, which is referred to as SPM (self-phase modulation). The quality of the pulse is therefore degraded and it is therefore difficult to use, for example during subsequent amplification. This SPM furthermore degrades the temporal profile of the pulse, which is detrimental to the final contrast.